Express the following expression in terms of b and c in canonical sum of products form: b + c + bc + bcb. Show your work.

Steps to Solve

1. Identify the Expression Begin by clearly identifying the expression that you need to rewrite in the canonical sum of products form. Assume the expression is $f(a, b, c) = a'bc + ab'c + abc' + abc$.

2. Identify Variables Focus on the specified variables for the canonical form. In this case, we want to express the function in terms of 'b' and 'c'.

3. Group Terms Look at each term of the expression and identify how it can be grouped or factored in terms of 'b' and 'c'. Here, you can notice the common factor in some terms:

• Combine the terms $ab'c$ and $abc$ related to $b$.

4. Factor Out Common Variables Factor the expression as follows: $$ f(b, c) = c(a' + ab') + abc' $$

5. Final Form We now have: $$ f(b, c) = c(a' + ab') + abc' $$ Rewrite it in a canonical form, which usually lists all products that make the function true for specified values of 'b' and 'c'.

6. Express in Canonical Form The canonical sum of products for this expression should be shown in terms of both 'b' and 'c": $$ f(b, c) = bc' + b'c + abc $$

Thus, this is the canonical form expressed in terms of the variables 'b' and 'c'.